The British secretary of state for international development, Hilary Benn, said on Monday the money would be used to buy up to 500 additional vehicles and to purchase more rapid-deployment equipment.
He said Britain had played a leading role in helping the AU mission. The initial contribution of £6.6 million was announced at the AU Donors' Conference in Addis Ababa on 26 May.
"As part of NATO's efforts to assist AMIS [African Union Mission in Sudan] expansion, the UK [United Kingdom] is also ready - subject to AU requirements and other donors' contributions - to support the airlift, co-ordinated by NATO, of up to three battalions into Darfur," Benn said.
The AU troops are helping to maintain a shaky ceasefire in Darfur where violence erupted in February 2003 when rebels took up arms in a bid to end what they said was state discrimination and marginalisation of the region's ethnic African inhabitants.
Although the AU troops have a limited capacity trying to secure a region the size of France, violence has subsided in the areas where they are deployed.
The AU has announced plans to increase its strength to 7,700 troops and civilian police, at a cost of $466 million.
Britain had also agreed to provide a Mobile Air Movements team of up to 15 people if required, Benn said.
Benn said Britain was also eager to support the civilian police contingent of the AU mission.
"We will support the EU's efforts to offer the AU a package of support, including training for the AU police and technical experts and advisers," he said.
He added, "We will also build accommodation for AU civilian police in camps for internally displaced people and villages, so that they can be deployed where they are needed most."
Benn also announced the appointment of Alan Goulty as Britain's special representative for Darfur.